TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

a__isLNat#(take(V1, V2))a__isNaturalKind#(V1)a__U181#(tt, V1)a__isLNatKind#(V1)
a__U271#(tt, V2)a__U272#(a__isLNatKind(V2))mark#(U201(X1, X2, X3))mark#(X1)
mark#(U294(X1, X2, X3))mark#(X1)a__U255#(tt, V2)a__isLNat#(V2)
mark#(U221(X))mark#(X)mark#(U33(X1, X2, X3))mark#(X1)
mark#(U204(X1, X2, X3))mark#(X1)a__isLNatKind#(natsFrom(V1))a__isNaturalKind#(V1)
a__take#(N, XS)a__U341#(a__isNatural(N), N, XS)mark#(U92(X1, X2))mark#(X1)
mark#(s(X))mark#(X)mark#(U243(X1, X2, X3))mark#(X1)
mark#(U326(X1, X2, X3, X4))mark#(X1)mark#(U193(X))a__U193#(mark(X))
mark#(U105(X1, X2))a__U105#(mark(X1), X2)a__U327#(pair(YS, ZS), X)mark#(ZS)
a__U111#(tt, V2)a__U112#(a__isLNatKind(V2))a__U254#(tt, V1, V2)a__isNatural#(V1)
mark#(U41(X1, X2, X3))mark#(X1)a__U42#(tt, V1, V2)a__U43#(a__isLNatKind(V2), V1, V2)
mark#(U312(X1, X2))mark#(X1)a__splitAt#(s(N), cons(X, XS))a__U321#(a__isNatural(N), N, X, XS)
a__U312#(tt, XS)mark#(XS)mark#(U11(X1, X2, X3))mark#(X1)
mark#(U45(X1, X2))mark#(X1)mark#(U231(X1, X2))a__U231#(mark(X1), X2)
a__U44#(tt, V1, V2)a__U45#(a__isNatural(V1), V2)mark#(U73(X))mark#(X)
a__U243#(tt, V1, V2)a__U244#(a__isLNatKind(V2), V1, V2)a__U326#(tt, N, X, XS)mark#(XS)
a__U181#(tt, V1)a__U182#(a__isLNatKind(V1), V1)a__U301#(tt, X, Y)a__U302#(a__isLNatKind(X), Y)
a__isLNat#(take(V1, V2))a__U101#(a__isNaturalKind(V1), V1, V2)a__isPLNatKind#(pair(V1, V2))a__isLNatKind#(V1)
mark#(U23(X1, X2, X3))a__U23#(mark(X1), X2, X3)mark#(U251(X1, X2, X3))mark#(X1)
mark#(U202(X1, X2, X3))mark#(X1)a__U324#(tt, N, X, XS)a__U325#(a__isLNat(XS), N, X, XS)
mark#(splitAt(X1, X2))mark#(X1)a__U21#(tt, X, Y)a__isLNatKind#(X)
mark#(isNatural(X))a__isNatural#(X)a__snd#(pair(X, Y))a__U301#(a__isLNat(X), X, Y)
mark#(U333(X1, X2))mark#(X1)a__U91#(tt, V1)a__isLNatKind#(V1)
mark#(U292(X1, X2, X3))a__U292#(mark(X1), X2, X3)mark#(U45(X1, X2))a__U45#(mark(X1), X2)
mark#(U253(X1, X2, X3))mark#(X1)a__U191#(tt, V1)a__U192#(a__isNaturalKind(V1), V1)
a__U253#(tt, V1, V2)a__isLNatKind#(V2)a__splitAt#(s(N), cons(X, XS))a__isNatural#(N)
a__U326#(tt, N, X, XS)a__splitAt#(mark(N), mark(XS))mark#(natsFrom(X))mark#(X)
a__U344#(tt, N, XS)a__fst#(a__splitAt(mark(N), mark(XS)))mark#(U56(X))a__U56#(mark(X))
a__U321#(tt, N, X, XS)a__isNaturalKind#(N)mark#(take(X1, X2))a__take#(mark(X1), mark(X2))
mark#(U255(X1, X2))mark#(X1)mark#(splitAt(X1, X2))a__splitAt#(mark(X1), mark(X2))
mark#(U191(X1, X2))mark#(X1)a__U326#(tt, N, X, XS)mark#(N)
a__U32#(tt, N, XS)a__U33#(a__isLNat(XS), N, XS)mark#(U192(X1, X2))a__U192#(mark(X1), X2)
a__U271#(tt, V2)a__isLNatKind#(V2)a__sel#(N, XS)a__isNatural#(N)
a__isNaturalKind#(head(V1))a__U211#(a__isLNatKind(V1))a__U121#(tt, V2)a__isLNatKind#(V2)
a__U332#(tt, XS)a__isLNat#(XS)a__U343#(tt, N, XS)a__U344#(a__isLNatKind(XS), N, XS)
mark#(U91(X1, X2))a__U91#(mark(X1), X2)a__U231#(tt, V2)a__U232#(a__isLNatKind(V2))
a__U43#(tt, V1, V2)a__U44#(a__isLNatKind(V2), V1, V2)mark#(U232(X))mark#(X)
a__U52#(tt, V1, V2)a__U53#(a__isLNatKind(V2), V1, V2)mark#(U71(X1, X2))a__U71#(mark(X1), X2)
a__U252#(tt, V1, V2)a__U253#(a__isLNatKind(V2), V1, V2)a__U51#(tt, V1, V2)a__isNaturalKind#(V1)
a__U54#(tt, V1, V2)a__U55#(a__isNatural(V1), V2)mark#(U71(X1, X2))mark#(X1)
a__sel#(N, XS)a__U291#(a__isNatural(N), N, XS)mark#(U31(X1, X2, X3))mark#(X1)
mark#(U121(X1, X2))mark#(X1)mark#(U42(X1, X2, X3))a__U42#(mark(X1), X2, X3)
mark#(U46(X))mark#(X)a__U34#(tt, N)mark#(N)
mark#(U11(X1, X2, X3))a__U11#(mark(X1), X2, X3)mark#(U343(X1, X2, X3))mark#(X1)
a__isLNat#(fst(V1))a__isPLNatKind#(V1)a__U311#(tt, XS)a__U312#(a__isLNatKind(XS), XS)
mark#(U93(X))a__U93#(mark(X))mark#(U204(X1, X2, X3))a__U204#(mark(X1), X2, X3)
a__isNatural#(head(V1))a__U181#(a__isLNatKind(V1), V1)mark#(U181(X1, X2))mark#(X1)
a__U321#(tt, N, X, XS)a__U322#(a__isNaturalKind(N), N, X, XS)mark#(U151(X))mark#(X)
a__U251#(tt, V1, V2)a__isNaturalKind#(V1)mark#(U93(X))mark#(X)
a__U33#(tt, N, XS)a__isLNatKind#(XS)a__U23#(tt, X, Y)a__U24#(a__isLNatKind(Y), X)
a__U11#(tt, N, XS)a__U12#(a__isNaturalKind(N), N, XS)a__U72#(tt, V1)a__isNatural#(V1)
mark#(U262(X))a__U262#(mark(X))mark#(tail(X))a__tail#(mark(X))
a__natsFrom#(N)a__U281#(a__isNatural(N), N)a__splitAt#(0, XS)a__U311#(a__isLNat(XS), XS)
a__U105#(tt, V2)a__U106#(a__isLNat(V2))a__U22#(tt, X, Y)a__U23#(a__isLNat(Y), X, Y)
mark#(U244(X1, X2, X3))mark#(X1)mark#(splitAt(X1, X2))mark#(X2)
mark#(U262(X))mark#(X)mark#(U312(X1, X2))a__U312#(mark(X1), X2)
mark#(U324(X1, X2, X3, X4))a__U324#(mark(X1), X2, X3, X4)mark#(U241(X1, X2, X3))a__U241#(mark(X1), X2, X3)
mark#(sel(X1, X2))a__sel#(mark(X1), mark(X2))a__U45#(tt, V2)a__isLNat#(V2)
a__U24#(tt, X)mark#(X)a__U41#(tt, V1, V2)a__U42#(a__isNaturalKind(V1), V1, V2)
mark#(U331(X1, X2, X3))mark#(X1)a__U203#(tt, V1, V2)a__U204#(a__isLNatKind(V2), V1, V2)
mark#(natsFrom(X))a__natsFrom#(mark(X))a__U81#(tt, V1)a__isPLNatKind#(V1)
a__U281#(tt, N)a__U282#(a__isNaturalKind(N), N)mark#(U281(X1, X2))mark#(X1)
a__U334#(tt, XS)mark#(XS)a__head#(cons(N, XS))a__U31#(a__isNatural(N), N, XS)
mark#(U192(X1, X2))mark#(X1)a__isLNat#(tail(V1))a__isLNatKind#(V1)
a__U21#(tt, X, Y)a__U22#(a__isLNatKind(X), X, Y)a__U82#(tt, V1)a__U83#(a__isPLNat(V1))
a__U71#(tt, V1)a__U72#(a__isNaturalKind(V1), V1)a__U104#(tt, V1, V2)a__isNatural#(V1)
a__U41#(tt, V1, V2)a__isNaturalKind#(V1)a__U302#(tt, Y)a__isLNat#(Y)
a__isLNatKind#(take(V1, V2))a__U171#(a__isNaturalKind(V1), V2)mark#(U231(X1, X2))mark#(X1)
a__U304#(tt, Y)mark#(Y)a__U344#(tt, N, XS)mark#(N)
a__isLNat#(snd(V1))a__U81#(a__isPLNatKind(V1), V1)a__snd#(pair(X, Y))a__isLNat#(X)
mark#(U52(X1, X2, X3))mark#(X1)mark#(U304(X1, X2))mark#(X1)
mark#(U282(X1, X2))mark#(X1)mark#(cons(X1, X2))mark#(X1)
mark#(U42(X1, X2, X3))mark#(X1)a__U31#(tt, N, XS)a__isNaturalKind#(N)
a__U204#(tt, V1, V2)a__isNatural#(V1)a__splitAt#(0, XS)a__isLNat#(XS)
mark#(U53(X1, X2, X3))mark#(X1)mark#(U101(X1, X2, X3))a__U101#(mark(X1), X2, X3)
mark#(U333(X1, X2))a__U333#(mark(X1), X2)mark#(U171(X1, X2))a__U171#(mark(X1), X2)
a__U341#(tt, N, XS)a__isNaturalKind#(N)mark#(U63(X))mark#(X)
mark#(U301(X1, X2, X3))a__U301#(mark(X1), X2, X3)a__U242#(tt, V1, V2)a__U243#(a__isLNatKind(V2), V1, V2)
a__U244#(tt, V1, V2)a__isLNat#(V1)a__U326#(tt, N, X, XS)a__U327#(a__splitAt(mark(N), mark(XS)), X)
a__isNatural#(head(V1))a__isLNatKind#(V1)mark#(U106(X))a__U106#(mark(X))
mark#(U73(X))a__U73#(mark(X))a__U255#(tt, V2)a__U256#(a__isLNat(V2))
a__U182#(tt, V1)a__U183#(a__isLNat(V1))mark#(U23(X1, X2, X3))mark#(X1)
mark#(U63(X))a__U63#(mark(X))mark#(U55(X1, X2))mark#(X1)
mark#(U323(X1, X2, X3, X4))mark#(X1)mark#(U181(X1, X2))a__U181#(mark(X1), X2)
mark#(U324(X1, X2, X3, X4))mark#(X1)a__U101#(tt, V1, V2)a__isNaturalKind#(V1)
mark#(U245(X1, X2))mark#(X1)a__U171#(tt, V2)a__U172#(a__isLNatKind(V2))
mark#(U102(X1, X2, X3))a__U102#(mark(X1), X2, X3)mark#(U293(X1, X2, X3))a__U293#(mark(X1), X2, X3)
mark#(U141(X))mark#(X)mark#(U327(X1, X2))a__U327#(mark(X1), X2)
a__U102#(tt, V1, V2)a__isLNatKind#(V2)mark#(U261(X1, X2))mark#(X1)
mark#(U31(X1, X2, X3))a__U31#(mark(X1), X2, X3)a__U55#(tt, V2)a__U56#(a__isLNat(V2))
mark#(U72(X1, X2))a__U72#(mark(X1), X2)mark#(U105(X1, X2))mark#(X1)
a__isPLNat#(splitAt(V1, V2))a__isNaturalKind#(V1)mark#(U51(X1, X2, X3))a__U51#(mark(X1), X2, X3)
a__U42#(tt, V1, V2)a__isLNatKind#(V2)a__U22#(tt, X, Y)a__isLNat#(Y)
mark#(U322(X1, X2, X3, X4))mark#(X1)a__U344#(tt, N, XS)mark#(XS)
a__U331#(tt, N, XS)a__isNaturalKind#(N)mark#(U255(X1, X2))a__U255#(mark(X1), X2)
a__U12#(tt, N, XS)a__isLNat#(XS)a__tail#(cons(N, XS))a__U331#(a__isNatural(N), N, XS)
mark#(U34(X1, X2))a__U34#(mark(X1), X2)a__U291#(tt, N, XS)a__isNaturalKind#(N)
mark#(U103(X1, X2, X3))mark#(X1)a__U14#(tt, N, XS)a__snd#(a__splitAt(mark(N), mark(XS)))
mark#(U112(X))a__U112#(mark(X))mark#(U34(X1, X2))mark#(X1)
mark#(U55(X1, X2))a__U55#(mark(X1), X2)a__U192#(tt, V1)a__U193#(a__isNatural(V1))
a__isNatural#(s(V1))a__U191#(a__isNaturalKind(V1), V1)a__U327#(pair(YS, ZS), X)mark#(X)
mark#(U81(X1, X2))a__U81#(mark(X1), X2)a__U282#(tt, N)mark#(N)
mark#(U303(X1, X2))a__U303#(mark(X1), X2)mark#(U106(X))mark#(X)
mark#(U281(X1, X2))a__U281#(mark(X1), X2)a__U241#(tt, V1, V2)a__isLNatKind#(V1)
mark#(U61(X1, X2))a__U61#(mark(X1), X2)a__isLNatKind#(fst(V1))a__U131#(a__isPLNatKind(V1))
mark#(U54(X1, X2, X3))a__U54#(mark(X1), X2, X3)a__U241#(tt, V1, V2)a__U242#(a__isLNatKind(V1), V1, V2)
mark#(U182(X1, X2))mark#(X1)a__U52#(tt, V1, V2)a__isLNatKind#(V2)
mark#(U21(X1, X2, X3))mark#(X1)a__isLNatKind#(cons(V1, V2))a__isNaturalKind#(V1)
a__U202#(tt, V1, V2)a__U203#(a__isLNatKind(V2), V1, V2)a__U281#(tt, N)a__isNaturalKind#(N)
mark#(U91(X1, X2))mark#(X1)a__isLNat#(fst(V1))a__U61#(a__isPLNatKind(V1), V1)
mark#(U83(X))a__U83#(mark(X))a__isNatural#(s(V1))a__isNaturalKind#(V1)
mark#(U201(X1, X2, X3))a__U201#(mark(X1), X2, X3)a__isLNatKind#(afterNth(V1, V2))a__isNaturalKind#(V1)
mark#(U141(X))a__U141#(mark(X))mark#(U327(X1, X2))mark#(X1)
a__isPLNatKind#(splitAt(V1, V2))a__isNaturalKind#(V1)a__U12#(tt, N, XS)a__U13#(a__isLNat(XS), N, XS)
mark#(U291(X1, X2, X3))mark#(X1)mark#(U271(X1, X2))mark#(X1)
a__U53#(tt, V1, V2)a__U54#(a__isLNatKind(V2), V1, V2)a__isLNatKind#(natsFrom(V1))a__U141#(a__isNaturalKind(V1))
a__U231#(tt, V2)a__isLNatKind#(V2)a__afterNth#(N, XS)a__U11#(a__isNatural(N), N, XS)
mark#(U242(X1, X2, X3))mark#(X1)a__U323#(tt, N, X, XS)a__isNaturalKind#(X)
mark#(U323(X1, X2, X3, X4))a__U323#(mark(X1), X2, X3, X4)mark#(isLNatKind(X))a__isLNatKind#(X)
a__fst#(pair(X, Y))a__U21#(a__isLNat(X), X, Y)a__U242#(tt, V1, V2)a__isLNatKind#(V2)
a__natsFrom#(N)a__isNatural#(N)mark#(U301(X1, X2, X3))mark#(X1)
mark#(U161(X))mark#(X)mark#(take(X1, X2))mark#(X2)
a__U254#(tt, V1, V2)a__U255#(a__isNatural(V1), V2)mark#(U282(X1, X2))a__U282#(mark(X1), X2)
mark#(U206(X))mark#(X)mark#(U83(X))mark#(X)
mark#(U253(X1, X2, X3))a__U253#(mark(X1), X2, X3)mark#(U46(X))a__U46#(mark(X))
mark#(U241(X1, X2, X3))mark#(X1)mark#(U334(X1, X2))mark#(X1)
a__U103#(tt, V1, V2)a__isLNatKind#(V2)a__U13#(tt, N, XS)a__isLNatKind#(XS)
mark#(U341(X1, X2, X3))a__U341#(mark(X1), X2, X3)a__U51#(tt, V1, V2)a__U52#(a__isNaturalKind(V1), V1, V2)
a__U331#(tt, N, XS)a__U332#(a__isNaturalKind(N), XS)mark#(U171(X1, X2))mark#(X1)
mark#(U326(X1, X2, X3, X4))a__U326#(mark(X1), X2, X3, X4)a__isNatural#(sel(V1, V2))a__U201#(a__isNaturalKind(V1), V1, V2)
a__isNatural#(sel(V1, V2))a__isNaturalKind#(V1)mark#(U12(X1, X2, X3))a__U12#(mark(X1), X2, X3)
a__U121#(tt, V2)a__U122#(a__isLNatKind(V2))mark#(U252(X1, X2, X3))a__U252#(mark(X1), X2, X3)
a__U102#(tt, V1, V2)a__U103#(a__isLNatKind(V2), V1, V2)mark#(sel(X1, X2))mark#(X1)
a__U43#(tt, V1, V2)a__isLNatKind#(V2)mark#(U121(X1, X2))a__U121#(mark(X1), X2)
mark#(U13(X1, X2, X3))mark#(X1)mark#(U202(X1, X2, X3))a__U202#(mark(X1), X2, X3)
a__U103#(tt, V1, V2)a__U104#(a__isLNatKind(V2), V1, V2)a__U201#(tt, V1, V2)a__U202#(a__isNaturalKind(V1), V1, V2)
a__U11#(tt, N, XS)a__isNaturalKind#(N)mark#(U254(X1, X2, X3))a__U254#(mark(X1), X2, X3)
mark#(afterNth(X1, X2))mark#(X1)mark#(U122(X))mark#(X)
a__U23#(tt, X, Y)a__isLNatKind#(Y)a__U55#(tt, V2)a__isLNat#(V2)
a__isLNatKind#(snd(V1))a__isPLNatKind#(V1)mark#(U221(X))a__U221#(mark(X))
mark#(U111(X1, X2))mark#(X1)a__U54#(tt, V1, V2)a__isNatural#(V1)
a__isLNatKind#(take(V1, V2))a__isNaturalKind#(V1)mark#(U161(X))a__U161#(mark(X))
mark#(U321(X1, X2, X3, X4))a__U321#(mark(X1), X2, X3, X4)mark#(U43(X1, X2, X3))mark#(X1)
a__U32#(tt, N, XS)a__isLNat#(XS)mark#(U62(X1, X2))mark#(X1)
mark#(U41(X1, X2, X3))a__U41#(mark(X1), X2, X3)a__U322#(tt, N, X, XS)a__isNatural#(X)
a__isLNat#(cons(V1, V2))a__U51#(a__isNaturalKind(V1), V1, V2)mark#(U243(X1, X2, X3))a__U243#(mark(X1), X2, X3)
mark#(head(X))mark#(X)mark#(isPLNat(X))a__isPLNat#(X)
a__isNaturalKind#(sel(V1, V2))a__isNaturalKind#(V1)mark#(fst(X))a__fst#(mark(X))
a__U205#(tt, V2)a__U206#(a__isLNat(V2))mark#(U242(X1, X2, X3))a__U242#(mark(X1), X2, X3)
a__U191#(tt, V1)a__isNaturalKind#(V1)mark#(fst(X))mark#(X)
a__U31#(tt, N, XS)a__U32#(a__isNaturalKind(N), N, XS)mark#(U82(X1, X2))mark#(X1)
a__U82#(tt, V1)a__isPLNat#(V1)a__U14#(tt, N, XS)mark#(N)
a__isLNat#(afterNth(V1, V2))a__U41#(a__isNaturalKind(V1), V1, V2)a__U171#(tt, V2)a__isLNatKind#(V2)
mark#(U311(X1, X2))a__U311#(mark(X1), X2)mark#(snd(X))mark#(X)
mark#(U21(X1, X2, X3))a__U21#(mark(X1), X2, X3)mark#(U22(X1, X2, X3))mark#(X1)
mark#(U122(X))a__U122#(mark(X))mark#(U53(X1, X2, X3))a__U53#(mark(X1), X2, X3)
mark#(U205(X1, X2))a__U205#(mark(X1), X2)a__U294#(tt, N, XS)a__head#(a__afterNth(mark(N), mark(XS)))
mark#(U44(X1, X2, X3))a__U44#(mark(X1), X2, X3)a__U261#(tt, V2)a__isLNatKind#(V2)
mark#(U232(X))a__U232#(mark(X))a__U243#(tt, V1, V2)a__isLNatKind#(V2)
mark#(take(X1, X2))mark#(X1)mark#(U172(X))mark#(X)
mark#(U304(X1, X2))a__U304#(mark(X1), X2)mark#(U54(X1, X2, X3))mark#(X1)
mark#(isNaturalKind(X))a__isNaturalKind#(X)mark#(U245(X1, X2))a__U245#(mark(X1), X2)
mark#(U246(X))mark#(X)a__U201#(tt, V1, V2)a__isNaturalKind#(V1)
a__isLNat#(snd(V1))a__isPLNatKind#(V1)a__U342#(tt, N, XS)a__isLNat#(XS)
mark#(U183(X))mark#(X)a__U192#(tt, V1)a__isNatural#(V1)
a__U323#(tt, N, X, XS)a__U324#(a__isNaturalKind(X), N, X, XS)mark#(U151(X))a__U151#(mark(X))
a__fst#(pair(X, Y))a__isLNat#(X)a__U72#(tt, V1)a__U73#(a__isNatural(V1))
a__U104#(tt, V1, V2)a__U105#(a__isNatural(V1), V2)mark#(U82(X1, X2))a__U82#(mark(X1), X2)
a__U182#(tt, V1)a__isLNat#(V1)a__U202#(tt, V1, V2)a__isLNatKind#(V2)
mark#(U104(X1, X2, X3))a__U104#(mark(X1), X2, X3)a__isLNatKind#(cons(V1, V2))a__U121#(a__isNaturalKind(V1), V2)
a__U333#(tt, XS)a__U334#(a__isLNatKind(XS), XS)a__U203#(tt, V1, V2)a__isLNatKind#(V2)
mark#(U103(X1, X2, X3))a__U103#(mark(X1), X2, X3)mark#(U61(X1, X2))mark#(X1)
mark#(U311(X1, X2))mark#(X1)mark#(U131(X))mark#(X)
mark#(U62(X1, X2))a__U62#(mark(X1), X2)a__U291#(tt, N, XS)a__U292#(a__isNaturalKind(N), N, XS)
mark#(U341(X1, X2, X3))mark#(X1)a__U342#(tt, N, XS)a__U343#(a__isLNat(XS), N, XS)
a__U33#(tt, N, XS)a__U34#(a__isLNatKind(XS), N)a__U13#(tt, N, XS)a__U14#(a__isLNatKind(XS), N, XS)
mark#(U325(X1, X2, X3, X4))mark#(X1)a__U325#(tt, N, X, XS)a__isLNatKind#(XS)
mark#(U172(X))a__U172#(mark(X))mark#(U102(X1, X2, X3))mark#(X1)
mark#(sel(X1, X2))mark#(X2)mark#(U14(X1, X2, X3))a__U14#(mark(X1), X2, X3)
mark#(U294(X1, X2, X3))a__U294#(mark(X1), X2, X3)mark#(U33(X1, X2, X3))a__U33#(mark(X1), X2, X3)
mark#(U12(X1, X2, X3))mark#(X1)mark#(U332(X1, X2))a__U332#(mark(X1), X2)
mark#(U24(X1, X2))mark#(X1)a__isLNatKind#(afterNth(V1, V2))a__U111#(a__isNaturalKind(V1), V2)
a__U244#(tt, V1, V2)a__U245#(a__isLNat(V1), V2)a__U341#(tt, N, XS)a__U342#(a__isNaturalKind(N), N, XS)
a__U61#(tt, V1)a__isPLNatKind#(V1)a__isNaturalKind#(sel(V1, V2))a__U231#(a__isNaturalKind(V1), V2)
mark#(U56(X))mark#(X)a__U111#(tt, V2)a__isLNatKind#(V2)
mark#(U271(X1, X2))a__U271#(mark(X1), X2)a__U245#(tt, V2)a__isLNat#(V2)
mark#(U205(X1, X2))mark#(X1)a__U91#(tt, V1)a__U92#(a__isLNatKind(V1), V1)
a__isLNat#(tail(V1))a__U91#(a__isLNatKind(V1), V1)a__U71#(tt, V1)a__isNaturalKind#(V1)
mark#(U342(X1, X2, X3))a__U342#(mark(X1), X2, X3)a__U14#(tt, N, XS)a__splitAt#(mark(N), mark(XS))
a__isLNatKind#(tail(V1))a__U161#(a__isLNatKind(V1))a__U324#(tt, N, X, XS)a__isLNat#(XS)
mark#(U101(X1, X2, X3))mark#(X1)a__U322#(tt, N, X, XS)a__U323#(a__isNatural(X), N, X, XS)
mark#(pair(X1, X2))mark#(X2)a__U252#(tt, V1, V2)a__isLNatKind#(V2)
mark#(U183(X))a__U183#(mark(X))a__U101#(tt, V1, V2)a__U102#(a__isNaturalKind(V1), V1, V2)
mark#(U22(X1, X2, X3))a__U22#(mark(X1), X2, X3)mark#(U131(X))a__U131#(mark(X))
mark#(U302(X1, X2))a__U302#(mark(X1), X2)mark#(U303(X1, X2))mark#(X1)
a__U204#(tt, V1, V2)a__U205#(a__isNatural(V1), V2)a__U253#(tt, V1, V2)a__U254#(a__isLNatKind(V2), V1, V2)
mark#(U344(X1, X2, X3))mark#(X1)a__isLNatKind#(tail(V1))a__isLNatKind#(V1)
mark#(U251(X1, X2, X3))a__U251#(mark(X1), X2, X3)a__isNaturalKind#(s(V1))a__U221#(a__isNaturalKind(V1))
a__U311#(tt, XS)a__isLNatKind#(XS)a__U303#(tt, Y)a__isLNatKind#(Y)
mark#(U72(X1, X2))mark#(X1)a__U292#(tt, N, XS)a__U293#(a__isLNat(XS), N, XS)
mark#(U256(X))mark#(X)a__isPLNatKind#(splitAt(V1, V2))a__U271#(a__isNaturalKind(V1), V2)
a__isLNat#(cons(V1, V2))a__isNaturalKind#(V1)mark#(pair(X1, X2))mark#(X1)
a__isNaturalKind#(head(V1))a__isLNatKind#(V1)a__isLNat#(natsFrom(V1))a__U71#(a__isNaturalKind(V1), V1)
mark#(tail(X))mark#(X)mark#(U13(X1, X2, X3))a__U13#(mark(X1), X2, X3)
a__U293#(tt, N, XS)a__U294#(a__isLNatKind(XS), N, XS)a__head#(cons(N, XS))a__isNatural#(N)
mark#(U206(X))a__U206#(mark(X))mark#(U203(X1, X2, X3))a__U203#(mark(X1), X2, X3)
mark#(U32(X1, X2, X3))a__U32#(mark(X1), X2, X3)mark#(afterNth(X1, X2))mark#(X2)
a__U325#(tt, N, X, XS)a__U326#(a__isLNatKind(XS), N, X, XS)mark#(U332(X1, X2))mark#(X1)
a__U92#(tt, V1)a__U93#(a__isLNat(V1))a__isLNatKind#(snd(V1))a__U151#(a__isPLNatKind(V1))
mark#(U292(X1, X2, X3))mark#(X1)a__U294#(tt, N, XS)a__afterNth#(mark(N), mark(XS))
a__afterNth#(N, XS)a__isNatural#(N)mark#(U14(X1, X2, X3))mark#(X1)
a__U294#(tt, N, XS)mark#(XS)a__U332#(tt, XS)a__U333#(a__isLNat(XS), XS)
mark#(U51(X1, X2, X3))mark#(X1)mark#(head(X))a__head#(mark(X))
a__U301#(tt, X, Y)a__isLNatKind#(X)a__U44#(tt, V1, V2)a__isNatural#(V1)
mark#(U302(X1, X2))mark#(X1)a__U61#(tt, V1)a__U62#(a__isPLNatKind(V1), V1)
a__tail#(cons(N, XS))a__isNatural#(N)mark#(U246(X))a__U246#(mark(X))
a__U343#(tt, N, XS)a__isLNatKind#(XS)a__U302#(tt, Y)a__U303#(a__isLNat(Y), Y)
mark#(U24(X1, X2))a__U24#(mark(X1), X2)mark#(U272(X))a__U272#(mark(X))
a__U293#(tt, N, XS)a__isLNatKind#(XS)a__U292#(tt, N, XS)a__isLNat#(XS)
a__U294#(tt, N, XS)mark#(N)mark#(U291(X1, X2, X3))a__U291#(mark(X1), X2, X3)
mark#(U92(X1, X2))a__U92#(mark(X1), X2)a__isPLNat#(pair(V1, V2))a__U241#(a__isLNatKind(V1), V1, V2)
mark#(afterNth(X1, X2))a__afterNth#(mark(X1), mark(X2))mark#(U32(X1, X2, X3))mark#(X1)
a__isLNat#(afterNth(V1, V2))a__isNaturalKind#(V1)mark#(U104(X1, X2, X3))mark#(X1)
a__take#(N, XS)a__isNatural#(N)a__isPLNat#(pair(V1, V2))a__isLNatKind#(V1)
mark#(U344(X1, X2, X3))a__U344#(mark(X1), X2, X3)mark#(U254(X1, X2, X3))mark#(X1)
a__isNaturalKind#(s(V1))a__isNaturalKind#(V1)a__U245#(tt, V2)a__U246#(a__isLNat(V2))
a__U261#(tt, V2)a__U262#(a__isLNatKind(V2))mark#(U191(X1, X2))a__U191#(mark(X1), X2)
a__isPLNatKind#(pair(V1, V2))a__U261#(a__isLNatKind(V1), V2)a__isPLNat#(splitAt(V1, V2))a__U251#(a__isNaturalKind(V1), V1, V2)
mark#(U81(X1, X2))mark#(X1)a__U205#(tt, V2)a__isLNat#(V2)
mark#(isLNat(X))a__isLNat#(X)a__U344#(tt, N, XS)a__splitAt#(mark(N), mark(XS))
a__U62#(tt, V1)a__isPLNat#(V1)mark#(U112(X))mark#(X)
mark#(snd(X))a__snd#(mark(X))a__U92#(tt, V1)a__isLNat#(V1)
mark#(U211(X))a__U211#(mark(X))a__U45#(tt, V2)a__U46#(a__isLNat(V2))
mark#(U321(X1, X2, X3, X4))mark#(X1)a__isLNatKind#(fst(V1))a__isPLNatKind#(V1)
mark#(U111(X1, X2))a__U111#(mark(X1), X2)mark#(U334(X1, X2))a__U334#(mark(X1), X2)
mark#(U203(X1, X2, X3))mark#(X1)mark#(U331(X1, X2, X3))a__U331#(mark(X1), X2, X3)
mark#(U252(X1, X2, X3))mark#(X1)a__U62#(tt, V1)a__U63#(a__isPLNat(V1))
mark#(U44(X1, X2, X3))mark#(X1)mark#(U256(X))a__U256#(mark(X))
a__U105#(tt, V2)a__isLNat#(V2)mark#(U244(X1, X2, X3))a__U244#(mark(X1), X2, X3)
mark#(isPLNatKind(X))a__isPLNatKind#(X)mark#(U325(X1, X2, X3, X4))a__U325#(mark(X1), X2, X3, X4)
mark#(U211(X))mark#(X)mark#(U52(X1, X2, X3))a__U52#(mark(X1), X2, X3)
mark#(U272(X))mark#(X)a__U53#(tt, V1, V2)a__isLNatKind#(V2)
mark#(U322(X1, X2, X3, X4))a__U322#(mark(X1), X2, X3, X4)mark#(U293(X1, X2, X3))mark#(X1)
a__U333#(tt, XS)a__isLNatKind#(XS)mark#(U342(X1, X2, X3))mark#(X1)
a__U251#(tt, V1, V2)a__U252#(a__isNaturalKind(V1), V1, V2)a__U303#(tt, Y)a__U304#(a__isLNatKind(Y), Y)
a__U81#(tt, V1)a__U82#(a__isPLNatKind(V1), V1)mark#(U193(X))mark#(X)
a__U14#(tt, N, XS)mark#(XS)mark#(U343(X1, X2, X3))a__U343#(mark(X1), X2, X3)
mark#(U43(X1, X2, X3))a__U43#(mark(X1), X2, X3)mark#(U182(X1, X2))a__U182#(mark(X1), X2)
a__isLNat#(natsFrom(V1))a__isNaturalKind#(V1)mark#(U261(X1, X2))a__U261#(mark(X1), X2)

Rewrite Rules

a__U101(tt, V1, V2)a__U102(a__isNaturalKind(V1), V1, V2)a__U102(tt, V1, V2)a__U103(a__isLNatKind(V2), V1, V2)
a__U103(tt, V1, V2)a__U104(a__isLNatKind(V2), V1, V2)a__U104(tt, V1, V2)a__U105(a__isNatural(V1), V2)
a__U105(tt, V2)a__U106(a__isLNat(V2))a__U106(tt)tt
a__U11(tt, N, XS)a__U12(a__isNaturalKind(N), N, XS)a__U111(tt, V2)a__U112(a__isLNatKind(V2))
a__U112(tt)tta__U12(tt, N, XS)a__U13(a__isLNat(XS), N, XS)
a__U121(tt, V2)a__U122(a__isLNatKind(V2))a__U122(tt)tt
a__U13(tt, N, XS)a__U14(a__isLNatKind(XS), N, XS)a__U131(tt)tt
a__U14(tt, N, XS)a__snd(a__splitAt(mark(N), mark(XS)))a__U141(tt)tt
a__U151(tt)tta__U161(tt)tt
a__U171(tt, V2)a__U172(a__isLNatKind(V2))a__U172(tt)tt
a__U181(tt, V1)a__U182(a__isLNatKind(V1), V1)a__U182(tt, V1)a__U183(a__isLNat(V1))
a__U183(tt)tta__U191(tt, V1)a__U192(a__isNaturalKind(V1), V1)
a__U192(tt, V1)a__U193(a__isNatural(V1))a__U193(tt)tt
a__U201(tt, V1, V2)a__U202(a__isNaturalKind(V1), V1, V2)a__U202(tt, V1, V2)a__U203(a__isLNatKind(V2), V1, V2)
a__U203(tt, V1, V2)a__U204(a__isLNatKind(V2), V1, V2)a__U204(tt, V1, V2)a__U205(a__isNatural(V1), V2)
a__U205(tt, V2)a__U206(a__isLNat(V2))a__U206(tt)tt
a__U21(tt, X, Y)a__U22(a__isLNatKind(X), X, Y)a__U211(tt)tt
a__U22(tt, X, Y)a__U23(a__isLNat(Y), X, Y)a__U221(tt)tt
a__U23(tt, X, Y)a__U24(a__isLNatKind(Y), X)a__U231(tt, V2)a__U232(a__isLNatKind(V2))
a__U232(tt)tta__U24(tt, X)mark(X)
a__U241(tt, V1, V2)a__U242(a__isLNatKind(V1), V1, V2)a__U242(tt, V1, V2)a__U243(a__isLNatKind(V2), V1, V2)
a__U243(tt, V1, V2)a__U244(a__isLNatKind(V2), V1, V2)a__U244(tt, V1, V2)a__U245(a__isLNat(V1), V2)
a__U245(tt, V2)a__U246(a__isLNat(V2))a__U246(tt)tt
a__U251(tt, V1, V2)a__U252(a__isNaturalKind(V1), V1, V2)a__U252(tt, V1, V2)a__U253(a__isLNatKind(V2), V1, V2)
a__U253(tt, V1, V2)a__U254(a__isLNatKind(V2), V1, V2)a__U254(tt, V1, V2)a__U255(a__isNatural(V1), V2)
a__U255(tt, V2)a__U256(a__isLNat(V2))a__U256(tt)tt
a__U261(tt, V2)a__U262(a__isLNatKind(V2))a__U262(tt)tt
a__U271(tt, V2)a__U272(a__isLNatKind(V2))a__U272(tt)tt
a__U281(tt, N)a__U282(a__isNaturalKind(N), N)a__U282(tt, N)cons(mark(N), natsFrom(s(N)))
a__U291(tt, N, XS)a__U292(a__isNaturalKind(N), N, XS)a__U292(tt, N, XS)a__U293(a__isLNat(XS), N, XS)
a__U293(tt, N, XS)a__U294(a__isLNatKind(XS), N, XS)a__U294(tt, N, XS)a__head(a__afterNth(mark(N), mark(XS)))
a__U301(tt, X, Y)a__U302(a__isLNatKind(X), Y)a__U302(tt, Y)a__U303(a__isLNat(Y), Y)
a__U303(tt, Y)a__U304(a__isLNatKind(Y), Y)a__U304(tt, Y)mark(Y)
a__U31(tt, N, XS)a__U32(a__isNaturalKind(N), N, XS)a__U311(tt, XS)a__U312(a__isLNatKind(XS), XS)
a__U312(tt, XS)pair(nil, mark(XS))a__U32(tt, N, XS)a__U33(a__isLNat(XS), N, XS)
a__U321(tt, N, X, XS)a__U322(a__isNaturalKind(N), N, X, XS)a__U322(tt, N, X, XS)a__U323(a__isNatural(X), N, X, XS)
a__U323(tt, N, X, XS)a__U324(a__isNaturalKind(X), N, X, XS)a__U324(tt, N, X, XS)a__U325(a__isLNat(XS), N, X, XS)
a__U325(tt, N, X, XS)a__U326(a__isLNatKind(XS), N, X, XS)a__U326(tt, N, X, XS)a__U327(a__splitAt(mark(N), mark(XS)), X)
a__U327(pair(YS, ZS), X)pair(cons(mark(X), YS), mark(ZS))a__U33(tt, N, XS)a__U34(a__isLNatKind(XS), N)
a__U331(tt, N, XS)a__U332(a__isNaturalKind(N), XS)a__U332(tt, XS)a__U333(a__isLNat(XS), XS)
a__U333(tt, XS)a__U334(a__isLNatKind(XS), XS)a__U334(tt, XS)mark(XS)
a__U34(tt, N)mark(N)a__U341(tt, N, XS)a__U342(a__isNaturalKind(N), N, XS)
a__U342(tt, N, XS)a__U343(a__isLNat(XS), N, XS)a__U343(tt, N, XS)a__U344(a__isLNatKind(XS), N, XS)
a__U344(tt, N, XS)a__fst(a__splitAt(mark(N), mark(XS)))a__U41(tt, V1, V2)a__U42(a__isNaturalKind(V1), V1, V2)
a__U42(tt, V1, V2)a__U43(a__isLNatKind(V2), V1, V2)a__U43(tt, V1, V2)a__U44(a__isLNatKind(V2), V1, V2)
a__U44(tt, V1, V2)a__U45(a__isNatural(V1), V2)a__U45(tt, V2)a__U46(a__isLNat(V2))
a__U46(tt)tta__U51(tt, V1, V2)a__U52(a__isNaturalKind(V1), V1, V2)
a__U52(tt, V1, V2)a__U53(a__isLNatKind(V2), V1, V2)a__U53(tt, V1, V2)a__U54(a__isLNatKind(V2), V1, V2)
a__U54(tt, V1, V2)a__U55(a__isNatural(V1), V2)a__U55(tt, V2)a__U56(a__isLNat(V2))
a__U56(tt)tta__U61(tt, V1)a__U62(a__isPLNatKind(V1), V1)
a__U62(tt, V1)a__U63(a__isPLNat(V1))a__U63(tt)tt
a__U71(tt, V1)a__U72(a__isNaturalKind(V1), V1)a__U72(tt, V1)a__U73(a__isNatural(V1))
a__U73(tt)tta__U81(tt, V1)a__U82(a__isPLNatKind(V1), V1)
a__U82(tt, V1)a__U83(a__isPLNat(V1))a__U83(tt)tt
a__U91(tt, V1)a__U92(a__isLNatKind(V1), V1)a__U92(tt, V1)a__U93(a__isLNat(V1))
a__U93(tt)tta__afterNth(N, XS)a__U11(a__isNatural(N), N, XS)
a__fst(pair(X, Y))a__U21(a__isLNat(X), X, Y)a__head(cons(N, XS))a__U31(a__isNatural(N), N, XS)
a__isLNat(nil)tta__isLNat(afterNth(V1, V2))a__U41(a__isNaturalKind(V1), V1, V2)
a__isLNat(cons(V1, V2))a__U51(a__isNaturalKind(V1), V1, V2)a__isLNat(fst(V1))a__U61(a__isPLNatKind(V1), V1)
a__isLNat(natsFrom(V1))a__U71(a__isNaturalKind(V1), V1)a__isLNat(snd(V1))a__U81(a__isPLNatKind(V1), V1)
a__isLNat(tail(V1))a__U91(a__isLNatKind(V1), V1)a__isLNat(take(V1, V2))a__U101(a__isNaturalKind(V1), V1, V2)
a__isLNatKind(nil)tta__isLNatKind(afterNth(V1, V2))a__U111(a__isNaturalKind(V1), V2)
a__isLNatKind(cons(V1, V2))a__U121(a__isNaturalKind(V1), V2)a__isLNatKind(fst(V1))a__U131(a__isPLNatKind(V1))
a__isLNatKind(natsFrom(V1))a__U141(a__isNaturalKind(V1))a__isLNatKind(snd(V1))a__U151(a__isPLNatKind(V1))
a__isLNatKind(tail(V1))a__U161(a__isLNatKind(V1))a__isLNatKind(take(V1, V2))a__U171(a__isNaturalKind(V1), V2)
a__isNatural(0)tta__isNatural(head(V1))a__U181(a__isLNatKind(V1), V1)
a__isNatural(s(V1))a__U191(a__isNaturalKind(V1), V1)a__isNatural(sel(V1, V2))a__U201(a__isNaturalKind(V1), V1, V2)
a__isNaturalKind(0)tta__isNaturalKind(head(V1))a__U211(a__isLNatKind(V1))
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Original Signature

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